sensitivity analysis of transmission.pptx
- 1. Sensitivity analysis A sensitivity analysis is a technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions It is also known as the what – if analysis. It helps in analyzing how sensitive the output is, by the changes in one input while keeping the other inputs constant.
- 2. Principle • Sensitivity analysis works on the simple principle: Change the model and observe the behavior. The parameters that one needs to note while doing the above are: • A) Experimental design: It includes combination of parameters that are to be varied. This includes a check on which and how many parameters need to vary at a given point in time, assigning values (maximum and minimum levels) before the experiment, • B) What to vary: The different parameters that can be chosen to vary in the model could be: a) the number of activities b) the objective in relation to the risk assumed and the profits expected c) technical parameters d) number of constraints and its limits • C) What to observe: a) value of the decision variables b) value of the objective function between two strategies adopted
- 3. Measurement of sensitivity analysis Steps used to conduct sensitivity analysis: • Firstly the output is defined; say V1 a input value for which the sensitivity is to be measured. All the other inputs of the model are kept constant. • Then the value of the output at a new value of the input (V2) while keeping other inputs constant is calculated. • Find the percentage change in the output and the percentage change in the input. • The sensitivity is calculated by dividing the percentage change in output by the percentage change in input.
- 4. Example • Suppose that Y is the fuel consumption of a particular model of car. Suppose that the predictors are • 1. X1 — the weight of the car (min-max: 1800-2200 kg) • 2. X2 — the horse power (min-max: 150-160) • 3. X3 — the no. of cylinders (min-max: 3:5) Model equation Y= 0.25 + 0.05 X1 - 0.8 X2 + 0.01 X1 X3
- 5. Example Definition of a factor effect: The change in the mean response when the factor is changed from low to high.
- 6. Calculation of Effects: Main effect The effect of a factor is defined to be the change in the response Y for a change in the level of that factor. This is called a main effect. Effect of A
- 9. Actually it is plus but to cover the negative signs of AB
- 13. Sumamry
- 14. Methods of Sensitivity Analysis There are different methods to carry out the sensitivity analysis: • Modeling and simulation techniques • Scenario management tools through Microsoft excel There are mainly two approaches to analyzing sensitivity: • Local Sensitivity Analysis • Global Sensitivity Analysis
- 15. various techniques widely applied include: • Differential sensitivity analysis: It is also referred to the direct method. It involves solving simple partial derivatives to temporal sensitivity analysis. Although this method is computationally efficient, solving equations is intensive task to handle. • One at a time sensitivity measures: It is the most fundamental method with partial differentiation, in which varying parameters values are taken one at a time. It is also called as local analysis as it is an indicator only for the addressed point estimates and not the entire distribution. • Factorial Analysis: It involves the selection of given number of samples for a specific parameter and then running the model for the combinations. The outcome is then used to carry out parameter sensitivity. • Through the sensitivity index one can calculate the output % difference when one input parameter varies from minimum to maximum value. • Correlation analysis helps in defining the relation between independent and dependent variables. • Regression analysis is a comprehensive method used to get responses for complex models. • Subjective sensitivity analysis: In this method the individual parameters are analyzed. This is a subjective method, simple, qualitative and an easy method to rule out input parameters.
- 16. Search techniques- univariate/multivariate • Univariate- One variable is analyzed at a time. Objective is to describe the variable. Example- How many students are graduating with “Analytics“ degree? • Bivariate- Two variables are analyzed together for any possible association or empirical relationship. Example- What is the correlation between “Gender” and graduation with “Analytics” degree? • Multivariate- More than two variables are analyzed together for any possible association or interactions. Example – What is correlation between “Gender”, “Country of Residence” and graduation with “ Analytics” degree? Any statistical modeling exercise such as Regression, Decision Tree, Clustering are multivariate in nature